Analysis of a hierarchical cellular system with reneging and dropping for waiting new and handoff calls

We analyze a hierarchical cellular system with finite queues for new and handoff calls. Both the effect of the reneging of waiting new calls because of the callers' impatience and the effect of the dropping of queued handoff calls as the callers move out of the handoff area are considered, besides the effect of the guard channel scheme. We successfully solve the system by adopting the multidimensional Markovian chain and using the transition-probability matrix and the signal-flow graph to obtain the average new-call blocking probability, the forced termination probability, and the average waiting time of queued new and handoff calls. We further investigate how the design parameters of the buffer sizes and guard channel numbers in macrocell and microcells affect the performance of the hierarchical cellular system. The results show that provision of a buffering scheme and guard channel scheme can effectively reduce the new call blocking probability and the forced termination probability in the hierarchical cellular system, and the effectiveness is more significant in the macrocell than in the microcells.